[Legatus]

New VatII form of Absolution:

"God, the Father of mercies, through the death and resurrection of His Son, has reconciled the world to Himself and sent the Holy Spirit among us for the forgiveness of sins; through the ministry of the Church may God give you pardon and peace, and I absolve you from your sins in the name of the Father, and of the Son, and of the Holy Spirit."

Traditional, pre-VatII form:

“May Almighty God have mercy on thee, forgive thee thy sins, and bring thee to everlasting life. Amen. May the almighty and merciful Lord grant thee pardon, absolution and remission of thy sins. May Our Lord Jesus Christ absolve thee, and I by His authority do absolve thee from every bond of excommunication, or interdict as far as I am able and thou art needful.

Notice any differences?

It is the traditional form that the author of this piece is arguing against. "Absolve" comes from the Latin word for "loosen", just so we are all on the same page as to the words being used. I prefer going to Confession in the traditional form...

[Legatus]

I missed the fun part because of editing issues, here it is:

May the passion of our Lord Jesus Christ, the merits of the blessed Virgin Mary and of all the saints, whatever good you have done and whatever evil you have endured achieve for you the forgiveness of your sins, the increase of grace, and the reward of everlasting life. Amen.

I absolve you from all censures and sins, in the name of the Father, and of the Son, + and of the Holy Ghost. Amen.

[NRx]

Here is the Orthodox formula from the Russian/Slavic Tradition...

O Lord God of the salvation of Your servants, merciful, compassionate and long-suffering; Who repents concerning our evil deeds, not desiring the death of a sinner, but that he should turn from his way and live. Show mercy now on Your servant [name] and grant to him (or her) an image of repentance, forgiveness of sins and deliverance, pardoning all his (or her) sins, whether voluntary or involuntary. Reconcile and unite him (or her) to Your Holy Church, through Jesus Christ our Lord, to Whom, with You, are due dominion and majesty, now and ever and unto ages of ages. Amen.

May our Lord and God, Jesus Christ, by the grace and compassion of His love for mankind, forgive you, my child, [name], all your transgressions. And I His unworthy Priest, through the power given me, forgive and absolve you from all your sins, in the Name of the Father, and of the Son, and of the Holy Spirit. Amen.

The Greeks use a slightly different formula.